Chern-Simons type cross-correlations and geometric Born effective charge of phonons

TL;DR

This paper explores how geometric Berry curvature influences phonon spectra and dynamics, revealing a new Chern-Simons-like coupling that enables phonon-photon interactions and offers novel ways to probe quantum geometry.

Contribution

It uncovers a previously overlooked Chern-Simons-like cross-correlation in 2+1D systems that links phonons and photons via a geometric Born effective charge.

Findings

Berry curvature affects optical phonon spectra.

Identifies a Chern-Simons-like cross-correlation dependent on valley Chern number.

Proposes a new method for coherent Raman phonon excitation.

Abstract

The interplay between different degrees of freedom in condensed matter systems engenders a rich variety of emergent phenomena. In particular, fermions with non-trivial quantum geometry can generate Chern-Simons (CS)-like terms in effective field theories for different gauge fields. For phonons, such terms can result in chiral phonon splitting. Here, we propose that the local Berry curvature can influence the spectra and dynamics of optical phonons, even in materials with zero Chern number, which we demonstrate with a gapped Dirac model. We identify a previously overlooked CS like cross-correlation between electromagnetic and pseudo-gauge fields in 2+1 dimensions which depends on valley Chern number. It facilitates a direct coupling between phonons and photons by inducing a geometric Born effective charge. This opens up a new route for coherent Raman phonon excitation and quantum geometry probes.